This book is devoted to the consistent and systematic application of
group theory to quantum mechanics. Beginning with a detailed
introduction to the classical theory of groups, Dr. Weyl continues with
an account of the fundamental results of quantum physics. There follows
a rigorous investigation of the relations holding between the
mathematical and physical theories.
Topics covered include: unitary geometry, quantum theory (Schrödinger's
wave equation, transition probabilities, directional quantization,
collision phenomena, Zeeman and Stark effects); groups and their
representations (sub-groups and conjugate classes, linear
transformations, rotation and Lorentz groups, closed continuous groups,
invariants and covariants, Lie's theory); applications of group theory
to quantum mechanics (simple state and term analysis, the spinning
electron, multiplet structure, energy and momentum, Pauli exclusion
principle, problem of several bodies, Maxwell-Dirac field equations,
etc.); the symmetric permutation group; and algebra of symmetric
transformation (invariant sub-spaces in group and tensor space,
sub-groups, Young's symmetry operators, spin and valence, group
theoretic classification of atomic spectra, branching laws, etc).
Throughout, Dr. Weyl emphasizes the reciprocity between representations
of the symmetric permutation group and those of the complete linear
group. His simplified treatment of reciprocity, the Clebsch-Gordan
series, and the Jordan-Hölder theorem and its analogues, has helped to
clarity these and other complex topics.
